---
_id: '63605'
alternative_title:
- Trends in Mathematics
author:
- first_name: "Tomasz\t"
  full_name: "Tomasz\tGoliński, Tomasz\t"
  last_name: "Tomasz\tGoliński"
- first_name: Praful
  full_name: Rahangdale, Praful
  id: '103300'
  last_name: Rahangdale
- first_name: Alice Barbora
  full_name: Tumpach, Alice Barbora
  last_name: Tumpach
citation:
  ama: "Tomasz\tGoliński T, Rahangdale P, Tumpach AB. Poisson structures in the Banach
    setting: comparison of different approaches. In: Kielanowski P, Dobrogowska A,
    Fernández D, Goliński D, eds. <i>Geometric Methods in Physics, XLI Workshop</i>.
    Geometric Methods in Physics XLI. Birkhauser; 2024:97–117. doi:<a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">10.1007/978-3-031-89857-0_9</a>"
  apa: "Tomasz\tGoliński, T., Rahangdale, P., &#38; Tumpach, A. B. (2024). Poisson
    structures in the Banach setting: comparison of different approaches. In P. Kielanowski,
    A. Dobrogowska, D. Fernández, &#38; D. Goliński (Eds.), <i>Geometric Methods in
    Physics, XLI Workshop</i> (pp. 97–117). Birkhauser. <a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">https://doi.org/10.1007/978-3-031-89857-0_9</a>"
  bibtex: "@inproceedings{Tomasz\tGoliński_Rahangdale_Tumpach_2024, place={Białowieża,
    Poland}, series={Geometric Methods in Physics XLI}, title={Poisson structures
    in the Banach setting: comparison of different approaches}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">10.1007/978-3-031-89857-0_9</a>},
    booktitle={Geometric Methods in Physics, XLI Workshop}, publisher={Birkhauser},
    author={Tomasz\tGoliński, Tomasz\t and Rahangdale, Praful and Tumpach, Alice Barbora},
    editor={Kielanowski, P. and Dobrogowska, A. and Fernández, D. and Goliński, D.},
    year={2024}, pages={97–117}, collection={Geometric Methods in Physics XLI} }"
  chicago: "Tomasz\tGoliński, Tomasz\t, Praful Rahangdale, and Alice Barbora Tumpach.
    “Poisson Structures in the Banach Setting: Comparison of Different Approaches.”
    In <i>Geometric Methods in Physics, XLI Workshop</i>, edited by P. Kielanowski,
    A. Dobrogowska, D. Fernández, and D. Goliński, 97–117. Geometric Methods in Physics
    XLI. Białowieża, Poland: Birkhauser, 2024. <a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">https://doi.org/10.1007/978-3-031-89857-0_9</a>."
  ieee: "T. Tomasz\tGoliński, P. Rahangdale, and A. B. Tumpach, “Poisson structures
    in the Banach setting: comparison of different approaches,” in <i>Geometric Methods
    in Physics, XLI Workshop</i>, Białystok, Poland, 2024, pp. 97–117, doi: <a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">10.1007/978-3-031-89857-0_9</a>."
  mla: "Tomasz\tGoliński, Tomasz, et al. “Poisson Structures in the Banach Setting:
    Comparison of Different Approaches.” <i>Geometric Methods in Physics, XLI Workshop</i>,
    edited by P. Kielanowski et al., Birkhauser, 2024, pp. 97–117, doi:<a href=\"https://doi.org/10.1007/978-3-031-89857-0_9\">10.1007/978-3-031-89857-0_9</a>."
  short: "T. Tomasz\tGoliński, P. Rahangdale, A.B. Tumpach, in: P. Kielanowski, A.
    Dobrogowska, D. Fernández, D. Goliński (Eds.), Geometric Methods in Physics, XLI
    Workshop, Birkhauser, Białowieża, Poland, 2024, pp. 97–117."
conference:
  end_date: 2024-07-06
  location: Białystok, Poland
  name: XLI Workshop on Geometric Methods in Physics
  start_date: 2024-07-01
date_created: 2026-01-14T01:54:48Z
date_updated: 2026-01-14T02:30:59Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/978-3-031-89857-0_9
editor:
- first_name: P.
  full_name: Kielanowski, P.
  last_name: Kielanowski
- first_name: A.
  full_name: Dobrogowska, A.
  last_name: Dobrogowska
- first_name: D.
  full_name: Fernández, D.
  last_name: Fernández
- first_name: D.
  full_name: Goliński, D.
  last_name: Goliński
language:
- iso: eng
page: 97–117
place: Białowieża, Poland
publication: Geometric Methods in Physics, XLI Workshop
publication_identifier:
  isbn:
  - 978-3-031-89857-0
publication_status: published
publisher: Birkhauser
series_title: Geometric Methods in Physics XLI
status: public
title: 'Poisson structures in the Banach setting: comparison of different approaches'
type: conference
user_id: '103300'
year: '2024'
...
---
_id: '34793'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Glöckner H, Hilgert J. Aspects of control theory on infinite-dimensional Lie
    groups and G-manifolds. <i>Journal of Differential Equations</i>. 2023;343:186–232.
    doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>
  apa: Glöckner, H., &#38; Hilgert, J. (2023). Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds. <i>Journal of Differential Equations</i>, <i>343</i>,
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>
  bibtex: '@article{Glöckner_Hilgert_2023, title={Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>},
    journal={Journal of Differential Equations}, author={Glöckner, Helge and Hilgert,
    Joachim}, year={2023}, pages={186–232} }'
  chicago: 'Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i> 343 (2023):
    186–232. <a href="https://doi.org/10.1016/j.jde.2022.10.001">https://doi.org/10.1016/j.jde.2022.10.001</a>.'
  ieee: 'H. Glöckner and J. Hilgert, “Aspects of control theory on infinite-dimensional
    Lie groups and G-manifolds,” <i>Journal of Differential Equations</i>, vol. 343,
    pp. 186–232, 2023, doi: <a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.'
  mla: Glöckner, Helge, and Joachim Hilgert. “Aspects of Control Theory on Infinite-Dimensional
    Lie Groups and G-Manifolds.” <i>Journal of Differential Equations</i>, vol. 343,
    2023, pp. 186–232, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.001">10.1016/j.jde.2022.10.001</a>.
  short: H. Glöckner, J. Hilgert, Journal of Differential Equations 343 (2023) 186–232.
date_created: 2022-12-21T19:31:13Z
date_updated: 2024-03-22T16:02:32Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
- _id: '91'
doi: 10.1016/j.jde.2022.10.001
external_id:
  arxiv:
  - '2007.11277'
intvolume: '       343'
keyword:
- '22E65'
- 28B05
- 34A12
- 34H05
- '46E30'
- '46E40'
language:
- iso: eng
page: 186–232
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
quality_controlled: '1'
status: public
title: Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
type: journal_article
user_id: '178'
volume: 343
year: '2023'
...
---
_id: '34803'
article_number: '50'
author:
- first_name: Elena
  full_name: Celledoni, Elena
  last_name: Celledoni
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Jørgen
  full_name: Riseth, Jørgen
  last_name: Riseth
- first_name: Alexander
  full_name: Schmeding, Alexander
  last_name: Schmeding
citation:
  ama: Celledoni E, Glöckner H, Riseth J, Schmeding A. Deep neural networks on diffeomorphism
    groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>.
    2023;63. doi:<a href="https://doi.org/10.1007/s10543-023-00989-05">10.1007/s10543-023-00989-05</a>
  apa: Celledoni, E., Glöckner, H., Riseth, J., &#38; Schmeding, A. (2023). Deep neural
    networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT
    Numerical Mathematics</i>, <i>63</i>, Article 50. <a href="https://doi.org/10.1007/s10543-023-00989-05">https://doi.org/10.1007/s10543-023-00989-05</a>
  bibtex: '@article{Celledoni_Glöckner_Riseth_Schmeding_2023, title={Deep neural networks
    on diffeomorphism groups for optimal shape reparametrization}, volume={63}, DOI={<a
    href="https://doi.org/10.1007/s10543-023-00989-05">10.1007/s10543-023-00989-05</a>},
    number={50}, journal={BIT Numerical Mathematics}, publisher={Springer}, author={Celledoni,
    Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}, year={2023}
    }'
  chicago: Celledoni, Elena, Helge Glöckner, Jørgen Riseth, and Alexander Schmeding.
    “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.”
    <i>BIT Numerical Mathematics</i> 63 (2023). <a href="https://doi.org/10.1007/s10543-023-00989-05">https://doi.org/10.1007/s10543-023-00989-05</a>.
  ieee: 'E. Celledoni, H. Glöckner, J. Riseth, and A. Schmeding, “Deep neural networks
    on diffeomorphism groups for optimal shape reparametrization,” <i>BIT Numerical
    Mathematics</i>, vol. 63, Art. no. 50, 2023, doi: <a href="https://doi.org/10.1007/s10543-023-00989-05">10.1007/s10543-023-00989-05</a>.'
  mla: Celledoni, Elena, et al. “Deep Neural Networks on Diffeomorphism Groups for
    Optimal Shape Reparametrization.” <i>BIT Numerical Mathematics</i>, vol. 63, 50,
    Springer, 2023, doi:<a href="https://doi.org/10.1007/s10543-023-00989-05">10.1007/s10543-023-00989-05</a>.
  short: E. Celledoni, H. Glöckner, J. Riseth, A. Schmeding, BIT Numerical Mathematics
    63 (2023).
date_created: 2022-12-22T07:37:20Z
date_updated: 2024-08-09T08:48:06Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s10543-023-00989-05
external_id:
  arxiv:
  - '2207.11141'
intvolume: '        63'
language:
- iso: eng
publication: BIT Numerical Mathematics
publisher: Springer
quality_controlled: '1'
status: public
title: Deep neural networks on diffeomorphism groups for optimal shape reparametrization
type: journal_article
user_id: '178'
volume: 63
year: '2023'
...
---
_id: '34805'
abstract:
- lang: eng
  text: "Let $E$ be a finite-dimensional real vector space and $M\\subseteq E$ be
    a\r\nconvex polytope with non-empty interior. We turn the group of all\r\n$C^\\infty$-diffeomorphisms
    of $M$ into a regular Lie group."
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Diffeomorphism groups of convex polytopes. <i>Journal of Convex
    Analysis</i>. 2023;30(1):343-358.
  apa: Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. <i>Journal
    of Convex Analysis</i>, <i>30</i>(1), 343–358.
  bibtex: '@article{Glöckner_2023, title={Diffeomorphism groups of convex polytopes},
    volume={30}, number={1}, journal={Journal of Convex Analysis}, publisher={Heldermann},
    author={Glöckner, Helge}, year={2023}, pages={343–358} }'
  chicago: 'Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal
    of Convex Analysis</i> 30, no. 1 (2023): 343–58.'
  ieee: H. Glöckner, “Diffeomorphism groups of convex polytopes,” <i>Journal of Convex
    Analysis</i>, vol. 30, no. 1, pp. 343–358, 2023.
  mla: Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of
    Convex Analysis</i>, vol. 30, no. 1, Heldermann, 2023, pp. 343–58.
  short: H. Glöckner, Journal of Convex Analysis 30 (2023) 343–358.
date_created: 2022-12-22T07:45:13Z
date_updated: 2024-08-09T08:49:17Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2203.09285'
intvolume: '        30'
issue: '1'
language:
- iso: eng
page: 343-358
publication: Journal of Convex Analysis
publisher: Heldermann
quality_controlled: '1'
status: public
title: Diffeomorphism groups of convex polytopes
type: journal_article
user_id: '178'
volume: 30
year: '2023'
...
---
_id: '34801'
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Luis
  full_name: Tárrega, Luis
  last_name: Tárrega
citation:
  ama: Glöckner H, Tárrega L. Mapping groups associated with real-valued function
    spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>.
    2023;33(1):271-296.
  apa: Glöckner, H., &#38; Tárrega, L. (2023). Mapping groups associated with real-valued
    function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>,
    <i>33</i>(1), 271–296.
  bibtex: '@article{Glöckner_Tárrega_2023, title={Mapping groups associated with real-valued
    function spaces and direct limits of Sobolev-Lie groups }, volume={33}, number={1},
    journal={Journal of Lie Theory}, publisher={Heldermann}, author={Glöckner, Helge
    and Tárrega, Luis}, year={2023}, pages={271–296} }'
  chicago: 'Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued
    Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i>
    33, no. 1 (2023): 271–96.'
  ieee: H. Glöckner and L. Tárrega, “Mapping groups associated with real-valued function
    spaces and direct limits of Sobolev-Lie groups ,” <i>Journal of Lie Theory</i>,
    vol. 33, no. 1, pp. 271–296, 2023.
  mla: Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued
    Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i>,
    vol. 33, no. 1, Heldermann, 2023, pp. 271–96.
  short: H. Glöckner, L. Tárrega, Journal of Lie Theory 33 (2023) 271–296.
date_created: 2022-12-22T07:23:57Z
date_updated: 2024-08-09T08:48:51Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2210.01246'
intvolume: '        33'
issue: '1'
language:
- iso: eng
page: 271-296
publication: Journal of Lie Theory
publisher: Heldermann
quality_controlled: '1'
status: public
title: 'Mapping groups associated with real-valued function spaces and direct limits
  of Sobolev-Lie groups '
type: journal_article
user_id: '178'
volume: 33
year: '2023'
...
---
_id: '55575'
author:
- first_name: Johanna
  full_name: Jakob, Johanna
  last_name: Jakob
citation:
  ama: Jakob J. Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen. Published
    online 2023.
  apa: Jakob, J. (2023). <i>Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen</i>.
  bibtex: '@article{Jakob_2023, title={Der Whitneysche Fortsetzungssatz für vektorwertige
    Funktionen}, author={Jakob, Johanna}, year={2023} }'
  chicago: Jakob, Johanna. “Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen,”
    2023.
  ieee: J. Jakob, “Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen.”
    2023.
  mla: Jakob, Johanna. <i>Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen</i>.
    2023.
  short: J. Jakob, (2023).
date_created: 2024-08-09T09:15:06Z
date_updated: 2024-08-09T09:27:43Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2307.03473'
language:
- iso: eng
status: public
title: Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen
type: preprint
user_id: '178'
year: '2023'
...
---
_id: '34814'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus.
    <i>Canadian Journal of Mathematics</i>. 2023;75(1):170-201. doi:<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>
  apa: Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential
    calculus. <i>Canadian Journal of Mathematics</i>, <i>75</i>(1), 170–201. <a href="https://doi.org/10.4153/s0008414x21000596">https://doi.org/10.4153/s0008414x21000596</a>
  bibtex: '@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s
    differential calculus}, volume={75}, DOI={<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>},
    number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical
    Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }'
  chicago: 'Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s
    Differential Calculus.” <i>Canadian Journal of Mathematics</i> 75, no. 1 (2023):
    170–201. <a href="https://doi.org/10.4153/s0008414x21000596">https://doi.org/10.4153/s0008414x21000596</a>.'
  ieee: 'M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential
    calculus,” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, pp. 170–201,
    2023, doi: <a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>.'
  mla: Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential
    Calculus.” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, Canadian Mathematical
    Society, 2023, pp. 170–201, doi:<a href="https://doi.org/10.4153/s0008414x21000596">10.4153/s0008414x21000596</a>.
  short: M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.
date_created: 2022-12-22T09:16:48Z
date_updated: 2023-02-22T11:38:32Z
department:
- _id: '93'
doi: 10.4153/s0008414x21000596
intvolume: '        75'
issue: '1'
keyword:
- extension of differentiable maps
language:
- iso: eng
page: 170-201
project:
- _id: '161'
  name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)'
publication: Canadian Journal of Mathematics
publication_identifier:
  issn:
  - 0008-414X
  - 1496-4279
publication_status: published
publisher: Canadian Mathematical Society
status: public
title: A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus
type: journal_article
user_id: '30905'
volume: 75
year: '2023'
...
---
_id: '34832'
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie
    Groups. <i>Annals of Global Analysis and Geometry</i>. 2023;63(21). doi:<a href="https://doi.org/10.1007/s10455-023-09888-y">10.1007/s10455-023-09888-y</a>
  apa: Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate
    Lie Groups. <i>Annals of Global Analysis and Geometry</i>, <i>63</i>(21). <a href="https://doi.org/10.1007/s10455-023-09888-y">https://doi.org/10.1007/s10455-023-09888-y</a>
  bibtex: '@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic
    Estimate Lie Groups}, volume={63}, DOI={<a href="https://doi.org/10.1007/s10455-023-09888-y">10.1007/s10455-023-09888-y</a>},
    number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch,
    Maximilian}, year={2023} }'
  chicago: Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic
    Estimate Lie Groups.” <i>Annals of Global Analysis and Geometry</i> 63, no. 21
    (2023). <a href="https://doi.org/10.1007/s10455-023-09888-y">https://doi.org/10.1007/s10455-023-09888-y</a>.
  ieee: 'M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate
    Lie Groups,” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023,
    doi: <a href="https://doi.org/10.1007/s10455-023-09888-y">10.1007/s10455-023-09888-y</a>.'
  mla: Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate
    Lie Groups.” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023,
    doi:<a href="https://doi.org/10.1007/s10455-023-09888-y">10.1007/s10455-023-09888-y</a>.
  short: M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).
date_created: 2022-12-22T09:45:34Z
date_updated: 2023-04-05T18:18:24Z
department:
- _id: '93'
doi: 10.1007/s10455-023-09888-y
intvolume: '        63'
issue: '21'
keyword:
- Lax equation
- generalized Baker-Campbell-Dynkin-Hausdorff formula
- regularity of Lie groups
language:
- iso: eng
project:
- _id: '161'
  name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)'
publication: Annals of Global Analysis and Geometry
publication_status: published
status: public
title: The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups
type: journal_article
user_id: '30905'
volume: 63
year: '2023'
...
---
_id: '34833'
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Decompositions of Analytic 1-Manifolds. <i>Indagationes Mathematicae</i>.
    2023;34(4):752-811. doi:<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>
  apa: Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. <i>Indagationes
    Mathematicae.</i>, <i>34</i>(4), 752–811. <a href="https://doi.org/10.1016/j.indag.2023.02.003">https://doi.org/10.1016/j.indag.2023.02.003</a>
  bibtex: '@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds},
    volume={34}, DOI={<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>},
    number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian},
    year={2023}, pages={752–811} }'
  chicago: 'Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes
    Mathematicae.</i> 34, no. 4 (2023): 752–811. <a href="https://doi.org/10.1016/j.indag.2023.02.003">https://doi.org/10.1016/j.indag.2023.02.003</a>.'
  ieee: 'M. Hanusch, “Decompositions of Analytic 1-Manifolds,” <i>Indagationes Mathematicae.</i>,
    vol. 34, no. 4, pp. 752–811, 2023, doi: <a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>.'
  mla: Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” <i>Indagationes
    Mathematicae.</i>, vol. 34, no. 4, 2023, pp. 752–811, doi:<a href="https://doi.org/10.1016/j.indag.2023.02.003">10.1016/j.indag.2023.02.003</a>.
  short: M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.
date_created: 2022-12-22T09:46:36Z
date_updated: 2023-05-25T07:32:38Z
department:
- _id: '93'
doi: 10.1016/j.indag.2023.02.003
intvolume: '        34'
issue: '4'
keyword:
- Lie group actions and analytic 1-submanifolds
language:
- iso: eng
page: 752-811
publication: Indagationes Mathematicae.
publication_status: published
status: public
title: Decompositions of Analytic 1-Manifolds
type: journal_article
user_id: '30905'
volume: 34
year: '2023'
...
---
_id: '34792'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Non-Lie subgroups in Lie groups over local fields of positive characteristic.
    <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>. 2022;14(2):138–144.
    doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>
  apa: Glöckner, H. (2022). Non-Lie subgroups in Lie groups over local fields of positive
    characteristic. <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    <i>14</i>(2), 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>
  bibtex: '@article{Glöckner_2022, title={Non-Lie subgroups in Lie groups over local
    fields of positive characteristic}, volume={14}, DOI={<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>},
    number={2}, journal={p-Adic Numbers, Ultrametric Analysis, and Applications},
    author={Glöckner, Helge}, year={2022}, pages={138–144} }'
  chicago: 'Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of
    Positive Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>
    14, no. 2 (2022): 138–144. <a href="https://doi.org/10.1134/S2070046622020042">https://doi.org/10.1134/S2070046622020042</a>.'
  ieee: 'H. Glöckner, “Non-Lie subgroups in Lie groups over local fields of positive
    characteristic,” <i>p-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, pp. 138–144, 2022, doi: <a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.'
  mla: Glöckner, Helge. “Non-Lie Subgroups in Lie Groups over Local Fields of Positive
    Characteristic.” <i>P-Adic Numbers, Ultrametric Analysis, and Applications</i>,
    vol. 14, no. 2, 2022, pp. 138–144, doi:<a href="https://doi.org/10.1134/S2070046622020042">10.1134/S2070046622020042</a>.
  short: H. Glöckner, P-Adic Numbers, Ultrametric Analysis, and Applications 14 (2022)
    138–144.
date_created: 2022-12-21T19:27:51Z
date_updated: 2022-12-21T19:30:25Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1134/S2070046622020042
intvolume: '        14'
issue: '2'
keyword:
- 20Exx
- 22Exx
- 32Cxx
language:
- iso: eng
page: 138–144
publication: p-Adic Numbers, Ultrametric Analysis, and Applications
publication_identifier:
  issn:
  - 2070-0466
quality_controlled: '1'
status: public
title: Non-Lie subgroups in Lie groups over local fields of positive characteristic
type: journal_article
user_id: '178'
volume: 14
year: '2022'
...
---
_id: '34791'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Alexander
  full_name: Schmeding, Alexander
  last_name: Schmeding
citation:
  ama: Glöckner H, Schmeding A. Manifolds of mappings on Cartesian products. <i>Annals
    of Global Analysis and Geometry</i>. 2022;61(2):359–398. doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>
  apa: Glöckner, H., &#38; Schmeding, A. (2022). Manifolds of mappings on Cartesian
    products. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(2), 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>
  bibtex: '@article{Glöckner_Schmeding_2022, title={Manifolds of mappings on Cartesian
    products}, volume={61}, DOI={<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>},
    number={2}, journal={Annals of Global Analysis and Geometry}, author={Glöckner,
    Helge and Schmeding, Alexander}, year={2022}, pages={359–398} }'
  chicago: 'Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i> 61, no. 2 (2022): 359–398.
    <a href="https://doi.org/10.1007/s10455-021-09816-y">https://doi.org/10.1007/s10455-021-09816-y</a>.'
  ieee: 'H. Glöckner and A. Schmeding, “Manifolds of mappings on Cartesian products,”
    <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, pp. 359–398, 2022,
    doi: <a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.'
  mla: Glöckner, Helge, and Alexander Schmeding. “Manifolds of Mappings on Cartesian
    Products.” <i>Annals of Global Analysis and Geometry</i>, vol. 61, no. 2, 2022,
    pp. 359–398, doi:<a href="https://doi.org/10.1007/s10455-021-09816-y">10.1007/s10455-021-09816-y</a>.
  short: H. Glöckner, A. Schmeding, Annals of Global Analysis and Geometry 61 (2022)
    359–398.
date_created: 2022-12-21T19:24:48Z
date_updated: 2022-12-21T19:27:09Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1007/s10455-021-09816-y
intvolume: '        61'
issue: '2'
keyword:
- 58D15
- '22E65'
- '26E15'
- '26E20'
- '46E40'
- 46T20
- 58A05
language:
- iso: eng
page: 359–398
publication: Annals of Global Analysis and Geometry
publication_identifier:
  issn:
  - 0232-704X
quality_controlled: '1'
status: public
title: Manifolds of mappings on Cartesian products
type: journal_article
user_id: '178'
volume: 61
year: '2022'
...
---
_id: '34796'
abstract:
- lang: eng
  text: 'We prove various results in infinite-dimensional differential calculus that
    relate the differentiability properties of functions and associated operator-valued
    functions (e.g., differentials). The results are applied in two areas: (1) in
    the theory of infinite-dimensional vector bundles, to construct new bundles from
    given ones, such as dual bundles, topological tensor products, infinite direct
    sums, and completions (under suitable hypotheses); (2) in the theory of locally
    convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity
    of passage from a function to the associated Hamiltonian vector field. Topological
    properties of topological vector spaces are essential for the studies, which allow
    the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter
    kR-spaces and locally convex spaces E such that E&times;E is a kR-space.'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>. 2022;11(5). doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>
  apa: Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>
  bibtex: '@article{Glöckner_2022, title={Aspects of differential calculus related
    to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11},
    DOI={<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>},
    number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }'
  chicago: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i> 11, no. 5 (2022). <a
    href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>.
  ieee: 'H. Glöckner, “Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi: <a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.'
  mla: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.
  short: H. Glöckner, Axioms 11 (2022).
date_created: 2022-12-21T20:02:29Z
date_updated: 2022-12-22T07:31:55Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.3390/axioms11050221
intvolume: '        11'
issue: '5'
language:
- iso: eng
publication: Axioms
publication_identifier:
  issn:
  - 2075-1680
quality_controlled: '1'
status: public
title: Aspects of differential calculus related to infinite-dimensional vector bundles
  and Poisson vector spaces
type: journal_article
user_id: '178'
volume: 11
year: '2022'
...
---
_id: '34804'
abstract:
- lang: eng
  text: "Starting with a finite-dimensional complex Lie algebra, we extend scalars\r\nusing
    suitable commutative topological algebras. We study Birkhoff\r\ndecompositions
    for the corresponding loop groups. Some results remain valid for\r\nloop groups
    with valued in complex Banach-Lie groups."
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Birkhoff decompositions for loop groups with coefficient algebras.
    <i>arXiv:220611711</i>. Published online 2022.
  apa: Glöckner, H. (2022). Birkhoff decompositions for loop groups with coefficient
    algebras. In <i>arXiv:2206.11711</i>.
  bibtex: '@article{Glöckner_2022, title={Birkhoff decompositions for loop groups
    with coefficient algebras}, journal={arXiv:2206.11711}, author={Glöckner, Helge},
    year={2022} }'
  chicago: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  ieee: H. Glöckner, “Birkhoff decompositions for loop groups with coefficient algebras,”
    <i>arXiv:2206.11711</i>. 2022.
  mla: Glöckner, Helge. “Birkhoff Decompositions for Loop Groups with Coefficient
    Algebras.” <i>ArXiv:2206.11711</i>, 2022.
  short: H. Glöckner, ArXiv:2206.11711 (2022).
date_created: 2022-12-22T07:42:07Z
date_updated: 2022-12-22T07:44:08Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2206.11711'
language:
- iso: eng
publication: arXiv:2206.11711
status: public
title: Birkhoff decompositions for loop groups with coefficient algebras
type: preprint
user_id: '178'
year: '2022'
...
---
_id: '34817'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>.
    2022;30(1):53-152. doi:<a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>
  apa: Hanusch, M. (2022). Regularity of Lie groups. <i>Communications in Analysis
    and Geometry</i>, <i>30</i>(1), 53–152. <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>
  bibtex: '@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={<a
    href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>},
    number={1}, journal={Communications in Analysis and Geometry}, publisher={International
    Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }'
  chicago: 'Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in
    Analysis and Geometry</i> 30, no. 1 (2022): 53–152. <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>.'
  ieee: 'M. Hanusch, “Regularity of Lie groups,” <i>Communications in Analysis and
    Geometry</i>, vol. 30, no. 1, pp. 53–152, 2022, doi: <a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>.'
  mla: Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis
    and Geometry</i>, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152,
    doi:<a href="https://doi.org/10.4310/cag.2022.v30.n1.a2">10.4310/cag.2022.v30.n1.a2</a>.
  short: M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.
date_created: 2022-12-22T09:19:43Z
date_updated: 2023-01-09T18:07:30Z
department:
- _id: '93'
doi: 10.4310/cag.2022.v30.n1.a2
extern: '1'
intvolume: '        30'
issue: '1'
keyword:
- regularity of Lie groups
language:
- iso: eng
page: 53-152
publication: Communications in Analysis and Geometry
publication_identifier:
  issn:
  - 1019-8385
  - 1944-9992
publication_status: published
publisher: International Press of Boston
status: public
title: Regularity of Lie groups
type: journal_article
user_id: '30905'
volume: 30
year: '2022'
...
---
_id: '34856'
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
  apa: Hanusch, M. (n.d.). <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  bibtex: '@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching},
    author={Hanusch, Maximilian} }'
  chicago: Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
    n.d.
  ieee: M. Hanusch, <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  mla: Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
  short: M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
    n.d.
date_created: 2022-12-22T17:06:02Z
date_updated: 2023-01-09T18:07:00Z
department:
- _id: '93'
language:
- iso: ger
page: '385'
publication_status: draft
publisher: https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
status: public
title: Analysis 1 und 2 Skript/Buch
type: working_paper
user_id: '30905'
year: '2022'
...
---
_id: '34786'
abstract:
- lang: eng
  text: A locally compact contraction group is a pair (G,α), where G is a locally
    compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We
    show that every surjective, continuous, equivariant homomorphism between locally
    compact contraction groups admits an equivariant continuous global section. As
    a consequence, extensions of locally compact contraction groups with abelian kernel
    can be described by continuous equivariant cohomology. For each prime number p,
    we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally
    disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0
    of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself.
    By contrast, there are only countably many locally compact contraction groups
    (up to isomorphism) which are torsion groups and abelian, as follows from a classification
    of the abelian locally compact contraction groups.
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: George A.
  full_name: Willis, George A.
  last_name: Willis
citation:
  ama: Glöckner H, Willis GA. Decompositions of locally compact contraction groups,
    series and extensions. <i>Journal of Algebra</i>. 2021;570:164-214. doi:<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>
  apa: Glöckner, H., &#38; Willis, G. A. (2021). Decompositions of locally compact
    contraction groups, series and extensions. <i>Journal of Algebra</i>, <i>570</i>,
    164–214. <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>
  bibtex: '@article{Glöckner_Willis_2021, title={Decompositions of locally compact
    contraction groups, series and extensions}, volume={570}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>},
    journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.},
    year={2021}, pages={164–214} }'
  chicago: 'Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact
    Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i> 570 (2021):
    164–214. <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.'
  ieee: 'H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction
    groups, series and extensions,” <i>Journal of Algebra</i>, vol. 570, pp. 164–214,
    2021, doi: <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.'
  mla: Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction
    Groups, Series and Extensions.” <i>Journal of Algebra</i>, vol. 570, 2021, pp.
    164–214, doi:<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.
  short: H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.
date_created: 2022-12-21T18:43:08Z
date_updated: 2022-12-21T18:58:44Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: https://doi.org/10.1016/j.jalgebra.2020.11.007
intvolume: '       570'
keyword:
- Contraction group
- Torsion group
- Extension
- Cocycle
- Section
- Equivariant cohomology
- Abelian group
- Nilpotent group
- Isomorphism types
language:
- iso: eng
page: 164-214
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
quality_controlled: '1'
status: public
title: Decompositions of locally compact contraction groups, series and extensions
type: journal_article
user_id: '178'
volume: 570
year: '2021'
...
---
_id: '34795'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Direct limits of regular Lie groups. <i>Mathematische Nachrichten</i>.
    2021;294(1):74–81. doi:<a href="https://doi.org/10.1002/mana.201900073">10.1002/mana.201900073</a>
  apa: Glöckner, H. (2021). Direct limits of regular Lie groups. <i>Mathematische
    Nachrichten</i>, <i>294</i>(1), 74–81. <a href="https://doi.org/10.1002/mana.201900073">https://doi.org/10.1002/mana.201900073</a>
  bibtex: '@article{Glöckner_2021, title={Direct limits of regular Lie groups}, volume={294},
    DOI={<a href="https://doi.org/10.1002/mana.201900073">10.1002/mana.201900073</a>},
    number={1}, journal={Mathematische Nachrichten}, author={Glöckner, Helge}, year={2021},
    pages={74–81} }'
  chicago: 'Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische
    Nachrichten</i> 294, no. 1 (2021): 74–81. <a href="https://doi.org/10.1002/mana.201900073">https://doi.org/10.1002/mana.201900073</a>.'
  ieee: 'H. Glöckner, “Direct limits of regular Lie groups,” <i>Mathematische Nachrichten</i>,
    vol. 294, no. 1, pp. 74–81, 2021, doi: <a href="https://doi.org/10.1002/mana.201900073">10.1002/mana.201900073</a>.'
  mla: Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische Nachrichten</i>,
    vol. 294, no. 1, 2021, pp. 74–81, doi:<a href="https://doi.org/10.1002/mana.201900073">10.1002/mana.201900073</a>.
  short: H. Glöckner, Mathematische Nachrichten 294 (2021) 74–81.
date_created: 2022-12-21T19:57:32Z
date_updated: 2022-12-21T20:00:29Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1002/mana.201900073
intvolume: '       294'
issue: '1'
language:
- iso: eng
page: 74–81
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
quality_controlled: '1'
status: public
title: Direct limits of regular Lie groups
type: journal_article
user_id: '178'
volume: 294
year: '2021'
...
---
_id: '34806'
abstract:
- lang: eng
  text: "Let $G$ be a Lie group over a totally disconnected local field and $\\alpha$\r\nbe
    an analytic endomorphism of $G$. The contraction group of $\\alpha$ ist the\r\nset
    of all $x\\in G$ such that $\\alpha^n(x)\\to e$ as $n\\to\\infty$. Call sequence\r\n$(x_{-n})_{n\\geq
    0}$ in $G$ an $\\alpha$-regressive trajectory for $x\\in G$ if\r\n$\\alpha(x_{-n})=x_{-n+1}$
    for all $n\\geq 1$ and $x_0=x$. The anti-contraction\r\ngroup of $\\alpha$ is
    the set of all $x\\in G$ admitting an $\\alpha$-regressive\r\ntrajectory $(x_{-n})_{n\\geq
    0}$ such that $x_{-n}\\to e$ as $n\\to\\infty$. The\r\nLevi subgroup is the set
    of all $x\\in G$ whose $\\alpha$-orbit is relatively\r\ncompact, and such that
    $x$ admits an $\\alpha$-regressive trajectory\r\n$(x_{-n})_{n\\geq 0}$ such that
    $\\{x_{-n}\\colon n\\geq 0\\}$ is relatively\r\ncompact. The big cell associated
    to $\\alpha$ is the set $\\Omega$ of all all\r\nproducts $xyz$ with $x$ in the
    contraction group, $y$ in the Levi subgroup and\r\n$z$ in the anti-contraction
    group. Let $\\pi$ be the mapping from the cartesian\r\nproduct of the contraction
    group, Levi subgroup and anti-contraction group to\r\n$\\Omega$ which maps $(x,y,z)$
    to $xyz$. We show: $\\Omega$ is open in $G$ and\r\n$\\pi$ is \\'{e}tale for suitable
    immersed Lie subgroup structures on the three\r\nsubgroups just mentioned. Moreover,
    we study group-theoretic properties of\r\ncontraction groups and anti-contraction
    groups."
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Contraction groups and the big cell for endomorphisms of Lie groups
    over  local fields. <i>arXiv:210102981</i>. Published online 2021.
  apa: Glöckner, H. (2021). Contraction groups and the big cell for endomorphisms
    of Lie groups over  local fields. In <i>arXiv:2101.02981</i>.
  bibtex: '@article{Glöckner_2021, title={Contraction groups and the big cell for
    endomorphisms of Lie groups over  local fields}, journal={arXiv:2101.02981}, author={Glöckner,
    Helge}, year={2021} }'
  chicago: Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms
    of Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021.
  ieee: H. Glöckner, “Contraction groups and the big cell for endomorphisms of Lie
    groups over  local fields,” <i>arXiv:2101.02981</i>. 2021.
  mla: Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of
    Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021.
  short: H. Glöckner, ArXiv:2101.02981 (2021).
date_created: 2022-12-22T07:47:35Z
date_updated: 2022-12-22T07:48:29Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
  arxiv:
  - '2101.02981'
language:
- iso: eng
publication: arXiv:2101.02981
status: public
title: Contraction groups and the big cell for endomorphisms of Lie groups over  local
  fields
type: preprint
user_id: '178'
year: '2021'
...
---
_id: '34818'
article_number: '101687'
article_type: original
author:
- first_name: Maximilian
  full_name: Hanusch, Maximilian
  id: '30905'
  last_name: Hanusch
citation:
  ama: Hanusch M. Symmetries of analytic curves. <i>Differential Geometry and its
    Applications</i>. 2021;74. doi:<a href="https://doi.org/10.1016/j.difgeo.2020.101687">10.1016/j.difgeo.2020.101687</a>
  apa: Hanusch, M. (2021). Symmetries of analytic curves. <i>Differential Geometry
    and Its Applications</i>, <i>74</i>, Article 101687. <a href="https://doi.org/10.1016/j.difgeo.2020.101687">https://doi.org/10.1016/j.difgeo.2020.101687</a>
  bibtex: '@article{Hanusch_2021, title={Symmetries of analytic curves}, volume={74},
    DOI={<a href="https://doi.org/10.1016/j.difgeo.2020.101687">10.1016/j.difgeo.2020.101687</a>},
    number={101687}, journal={Differential Geometry and its Applications}, publisher={Elsevier
    BV}, author={Hanusch, Maximilian}, year={2021} }'
  chicago: Hanusch, Maximilian. “Symmetries of Analytic Curves.” <i>Differential Geometry
    and Its Applications</i> 74 (2021). <a href="https://doi.org/10.1016/j.difgeo.2020.101687">https://doi.org/10.1016/j.difgeo.2020.101687</a>.
  ieee: 'M. Hanusch, “Symmetries of analytic curves,” <i>Differential Geometry and
    its Applications</i>, vol. 74, Art. no. 101687, 2021, doi: <a href="https://doi.org/10.1016/j.difgeo.2020.101687">10.1016/j.difgeo.2020.101687</a>.'
  mla: Hanusch, Maximilian. “Symmetries of Analytic Curves.” <i>Differential Geometry
    and Its Applications</i>, vol. 74, 101687, Elsevier BV, 2021, doi:<a href="https://doi.org/10.1016/j.difgeo.2020.101687">10.1016/j.difgeo.2020.101687</a>.
  short: M. Hanusch, Differential Geometry and Its Applications 74 (2021).
date_created: 2022-12-22T09:20:30Z
date_updated: 2023-01-09T18:07:26Z
department:
- _id: '93'
doi: 10.1016/j.difgeo.2020.101687
extern: '1'
intvolume: '        74'
keyword:
- Geometry and Topology
- Analysis
language:
- iso: eng
publication: Differential Geometry and its Applications
publication_identifier:
  issn:
  - 0926-2245
publication_status: published
publisher: Elsevier BV
status: public
title: Symmetries of analytic curves
type: journal_article
user_id: '30905'
volume: 74
year: '2021'
...
---
_id: '64765'
author:
- first_name: Natalie
  full_name: Nikitin, Natalie
  last_name: Nikitin
citation:
  ama: Nikitin N. <i>Regularity Properties of Infinite-Dimensional Lie Groups and
    Exponential Laws</i>.; 2021.
  apa: Nikitin, N. (2021). <i>Regularity properties of infinite-dimensional Lie groups
    and exponential laws</i>.
  bibtex: '@book{Nikitin_2021, title={Regularity properties of infinite-dimensional
    Lie groups and exponential laws}, author={Nikitin, Natalie}, year={2021} }'
  chicago: Nikitin, Natalie. <i>Regularity Properties of Infinite-Dimensional Lie
    Groups and Exponential Laws</i>, 2021.
  ieee: N. Nikitin, <i>Regularity properties of infinite-dimensional Lie groups and
    exponential laws</i>. 2021.
  mla: Nikitin, Natalie. <i>Regularity Properties of Infinite-Dimensional Lie Groups
    and Exponential Laws</i>. 2021.
  short: N. Nikitin, Regularity Properties of Infinite-Dimensional Lie Groups and
    Exponential Laws, 2021.
date_created: 2026-02-26T21:15:13Z
date_updated: 2026-02-26T21:15:28Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://nbn-resolving.org/urn:nbn:de:hbz:466:2-39133
oa: '1'
status: public
supervisor:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
title: Regularity properties of infinite-dimensional Lie groups and exponential laws
type: dissertation
user_id: '178'
year: '2021'
...